I would stay away from the World Wars and Cold War on WWIV map (ironically) -- all three of those wars had heavy European participation but the WWIV map is really awkward for that.
I'd instead recommend simply taking the modern scene, with these alliances and small tweaks:
North Atlantic Treaty Organization: Canada, Quebec, California, Texas, United States, Illinois, United Kingdom, Catholica, Germany, Turkey, Japan, Australia, Philippines
South American Defense Council: Colombia, Amazon Empire, Brazil, Peru, Argentina
Peace and Security Council: Egypt, Nigeria, Kenya, Congo, South Africa
Shanghai Cooperation Organisation: Russia, Central Asia, Sichuan Empire, Song Empire, Manchuria, Iran, India, Cuba
Neutral/Unaffiliated: Mexico, Thailand, Indonesia, Oceania
Same concept as the WWII team setup -- you have your main factions in NATO, SADC, PSC and SCO, and a few minor unaffiliated powers to woo. Neutral powers still can wing it solo, but unlike in WWII, they're allowed to join the major factions if they so choose. The reason for this is because the WWII game was designed to play out a balanced game of what already happened; we knew Turkey would stay neutral throughout because it did in WWII, so we made it stay neutral. Here we're playing from the present into the future, so we obviously don't know what the different powers are going to do. Thus, neutral powers can join the major factions. Once they join, though, they are permanent members (to keep the spirit of the team game intact).